The probability of conditionals: A review.

A major hypothesis about conditionals is the Equation in which the probability of a conditional equals the corresponding conditional probability: p(if A then C) = p(C|A). Probabilistic theories often treat it as axiomatic, whereas it follows from the meanings of conditionals in the theory of mental models. In this theory, intuitive models (system 1) do not represent what is false, and so produce errors in estimates of p(if A then C), yielding instead p(A & C). Deliberative models (system 2) are normative, and yield the proportion of cases of A in which C holds, i.e., the Equation. Intuitive estimates of the probability of a conditional about unique events: If covid-19 disappears in the USA, then Biden will run for a second term, together with those of each of its clauses, are liable to yield joint probability distributions that sum to over 100%. The error, which is inconsistent with the probability calculus, is massive when participants estimate the joint probabilities of conditionals with each of the different possibilities to which they refer. This result and others under review corroborate the model theory.

Can conditionals explain explanations? A modus ponens model of B because A.

We suggest a normative model for the evaluation of explanations B because A based on probabilistic conditional reasoning and compare it with empirical data. According to the modus ponens model of explanations, the probability of B because A should equal the joint probability of the conditional if A then B and the explanans A. We argue that B because A expresses the conjunction of A and B as well as positive relevance of A for B. In Study 1, participants (N = 80) judged the subjective probabilities of 20 sets of statements with a focus on belief-based reasoning under uncertainty. In Study 2, participants (N = 376) were assigned to one of six item sets for which we varied the inferential relevance of A for B to explore boundary conditions of our model. We assessed the performance of our model across a range of analyses and report results on the Equation, a fundamental model in research on probabilistic reasoning concerning the evaluation of conditionals. In both studies, results indicate that participants' belief in statements B because A followed model predictions systematically. However, a sizeable proportion of sets of beliefs contained at least one incoherence, indicating deviations from the norms of rationality suggested by our model. In addition, results of Study 2 lend support to the idea that inferential relevance may be relevant for the evaluation of both conditionals and explanations.

Derivation of the equation of isostatic line of compression and splitting force in a bottle-shaped strut.

The reported data deal with the derivation of the equation of isostatic line of compression (ILC) and splitting force in a bottle-shaped strut with different height-to-width ratios. The final data show that the splitting force in a bottle-shaped strut is not only related to the height-to-width ratio (h/b), but also related to the load area ratio.

Dynamic interfacial tension of surfactant solutions.

The dynamics of surfactant interfacial layers was first discussed more than a century ago. In 1946 the most important work by Ward and Tordai was published which is still the theoretical basis of all new models to describe the time dependence of interfacial properties. In addition to the diffusion controlled adsorption mechanism, many other models have been postulated in literature, however, well performed experiments with well defined surfactant systems have shown that the diffusional transport is the main process governing the entire formation of surfactant adsorption layers. The main prerequisite, in addition to the diffusional transport, is the consideration of the right boundary condition at the interface, given by a respective equation of state. In addition to the classical models of Langmuir and Frumkin, also the so-called reorientation or interfacial aggregation models are to be assumed to reach a quantitative description of respective experimental data. Moreover, the adsorption of surfactants at the interface between water and a gas phase different from air can be strongly influenced by the type of molecules within the gas phase, such as alkane vapours. These oil molecules co-adsorb from the gas phase and change the adsorption kinetics strongly. Besides the discussion of how to apply theoretical adsorption kinetics models correctly, a large number of experimental data are presented and the way of a quantitative analysis of the adsorption mechanism and the main characteristic parameters is presented. This includes micellar solutions as well as mixtures of surfactants of ionic and non-ionic nature.

Relevance and Reason Relations.

This paper examines precursors and consequents of perceived relevance of a proposition A for a proposition C. In Experiment 1, we test Spohn's (2012) assumption that ∆P = P(C|A) - P(C|~A) is a good predictor of ratings of perceived relevance and reason relations, and we examine whether it is a better predictor than the difference measure (P(C|A) - P(C)). In Experiment 2, we examine the effects of relevance on probabilistic coherence in Cruz, Baratgin, Oaksford, and Over's (2015) uncertain "and-to-if" inferences. The results suggest that ∆P predicts perceived relevance and reason relations better than the difference measure and that participants are either less probabilistically coherent in "and-to-if" inferences than initially assumed or that they do not follow P(if A, then C) = P(C|A) ("the Equation"). Results are discussed in light of recent results suggesting that the Equation may not hold under conditions of irrelevance or negative relevance.

The relevance effect and conditionals.

More than a decade of research has found strong evidence for P(if A, then C)=P(C|A) ("the Equation"). We argue, however, that this hypothesis provides an overly simplified picture due to its inability to account for relevance. We manipulated relevance in the evaluation of the probability and acceptability of indicative conditionals and found that relevance moderates the effect of P(C|A). This corroborates the Default and Penalty Hypothesis put forward in this paper. Finally, the probability and acceptability of concessive conditionals ("Even if A, then still C") were investigated and it was found that the Equation provides a better account of concessive conditionals than of indicatives across relevance manipulations.

[The reasons for the «space¼ of gerontology: the impact of the movements of the Earth and Moon on the performance of the human environment].

For future gerontological research specific interest are the research results obtained at the junction of Geophysics, astronomy, and biology, and existing links pointing to indicators of living objects with cosmophysical factors. The paper presents data on basic astronomical factors, potentially on a regular basis may cause gravitational effects on the biosphere as a living environment. Among these factors are movement of the Earth and Moon described is known in astronomy equations: the equation of the equinoxes, equation of time, as well as major perturbations from the Sun (evection, variation and annual inequality) inferred from the theory of lunar motion. Based on the amount of major perturbations from the Sun, the so-called λD-functions that are carried out to study the relationship between fluctuations of the so-called «computer time¼, the energy of solar radiation in the range of 605-607 nm, and the concentration of hemoglobin and red blood cells with major perturbations from the Sun. The resulting conclusion about the universal nature of the impact of the movements of the Moon and the Earth on the biosphere. The tables for the period from 01.01.2015 to 31.12.2016, with the calculated values λD functions that are potentially important for analyzing their association with temporal changes of various indicators of the body. The regularities obtained in the comparison of changes in various biomarkers with the course of values λD functions from tables, can be predictive in the study of the functioning of humans and the biosphere for astronomical periods. The research was carried out in Antarctica, where excluded the influence of artificial electromagnetic fields, st. Vostok (1998-1999) and st. Novolazarevskaya (2003-2004).